The publication first offers information on the motion of a rigid body around a fixed axis. Discussions focus on moment of inertia for a sphere for an axis through its center of gravity; moment of inertia of a cylinder for an axis through its center of gravity and normal to its axis of figure; and moment of inertia of a rectangular parallelepiped for an axis normal to one of its faces and through its center of gravity.

The text then elaborates on the general plane motion of a rigid body and some special problems involving friction. Topics include belt and rope friction, power transmitted by a flat disk coupling, friction in a flat step bearing, meaning of the general torque equation for plane motion, superelevation of the outer rail on a railway curve, kinetic energy, and equilibrium. The book takes a look at undamped simple harmonic motion and damped and forced oscillations, including vibrations with damping, compound pendulum, and amplitude of forced oscillations in the steady state.

The publication is a valuable source of data for students interested in plane rigid dynamics.

Contenu

Preface
Chapter One The Motion of a Rigid Body Around a Fixed Axis
The Rotation of a Rigid Body around a Fixed Axis
The Evaluation of the Moment of Inertia for Some Simple Figures
The Moment of Inertia of a Thin Rectangular Plate for a Polar Axis through Its Center of Gravity
The Moment of Inertia of a Rectangular Parallelepiped for an Axis Normal to One of Its Faces and through Its Center of Gravity
The Moment of Inertia of a Cylinder for an Axis through Its Center of Gravity and Normal to Its Axis of Figure
The Moment of Inertia for a Sphere for an Axis through Its Center of Gravity
A Note on the Quadratic Moment
Problems
The Conservation of Angular Momentum
The Gyroscope: A Problem in Angular Momentum
Rolling Motion
Use of the Instantaneous Center
A Rolling Body on an Inclined Plane
Problems
Chapter Two The General Plane Motion of A Rigid Body
The General Plane Motion of a Rigid Body
The Meaning of the General Torque Equation for Plane Motion
Note on the Inertial Forces
Pure Translation
The Superelevation of the Outer Rail on a Railway Curve
Equilibrium
Kinetic Energy
Problems
Chapter Three Some Special Problems Involving Friction
Belt and Rope Friction
Power Transmission by Belts
The Efficiency of Belt Transmission. Slip
The Friction in a Flat Step Bearing
Power Transmitted by a Flat Disk Coupling
Rolling Bodies-Limiting Condition for Rolling or Slipping
Problems
Chapter Four Undamped Simple Harmonic Motion
Definition of Simple Harmonic Motion
Definition of SHM
Definition of Some Quantities Associated with Vibratory Motion
The Quantitative Relations among Velocity, Displacement, and Period in SHM (Undamped)
A Mass Vibrating on a Spring
The Simple Pendulum
The Motion of the Projection on the Diameter of a Point Moving with Uniform Speed on a Circle
The Energy of a Body Vibrating with SHM
An Alternative Calculation of the Potential Energy
The Form of the Expression for the Period of SHM
A Useful Expression for the Period in Undamped Harmonic Motion in Terms of the Energy
Period for a Mass Hanging on a Heavy Spring
Angular Harmonic Motion
The Simple Pendulum
The Oscillations of a Magnet in a Magnetic Field
Comparison of Moments of Inertia
Measurement of Rigidity by a Kinetic Method
The Bifilar Pendulum
The Compound Pendulum
Condition for Minimum Period
The Center of Percussion
Problems
Chapter Five Damped Oscillations Forced Oscillations
Free Vibrations with Damping
The Logarithmic Decrement-Log dec
Energy
Forced Oscillations
The Amplitude of Forced Oscillations in the Steady State
Problems
Chapter Six Newton's Law of Gravitation
Kepler's Laws of Planetary Motion
Newton's Law of Universal Gravitation
The Gravitational Force Between a Uniform Spherical Shell and a Particle
The Gravitational Force between a Uniform Solid Sphere and a Particle
The Gravitational Force on a Particle Which Is within a Uniform Spherical Shell
Gauss' Law of Total Outward Normal Flux
The Acceleration due to Gravity and the Mass of the Earth
The Variation of the Acceleration of a Freely Falling Body with Its Distance from the Earth
The Time to Fall from a Great Height to the Surface of the Earth
The Gravitational Potential Due to the Earth
Kepler's Law of Areal Velocity
The Equation of the Path of a Particle under an Inverse Square Law of Force
Kepler's Harmonic Law
The Total Energy of a Planet Which is Moving in an Orbit
Problems
Answers
Subject Index